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Bending of a tube with a transverse hole

Bending of a tube with a transverse hole D d σ max M M d i
Bending of a tube with a transverse hole

Values for calculation

$M$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$d_i$ $\mathrm{mm}$
$d$ $\mathrm{mm}$

Calculation

Coefficient $ C_1 $

$$C_1=3$$
$C_1=3$
Equations in LaTeX code
C_1=3

Coefficient $ C_2 $

$$C_2=-6.25-0.585\cdot\left(\cfrac{d_i}{D}\right)+3.115\cdot\left(\cfrac{d_i}{D}\right)^2$$
$C_2=-6.25-0.585\cdot\left(\cfrac{d_i}{D}\right)+3.115\cdot\left(\cfrac{d_i}{D}\right)^2$
Equations in LaTeX code
C_2=-6.25-0.585\cdot\left(\cfrac{d_i}{D}\right)+3.115\cdot\left(\cfrac{d_i}{D}\right)^2

Coefficient $ C_3 $

$$C_3=41-1.071\cdot\left(\cfrac{d_i}{D}\right)-6.746\cdot\left(\cfrac{d_i}{D}\right)^2$$
$C_3=41-1.071\cdot\left(\cfrac{d_i}{D}\right)-6.746\cdot\left(\cfrac{d_i}{D}\right)^2$
Equations in LaTeX code
C_3=41-1.071\cdot\left(\cfrac{d_i}{D}\right)-6.746\cdot\left(\cfrac{d_i}{D}\right)^2

Coefficient $ C_4 $

$$C_4=-45+1.389\cdot\left(\cfrac{d_i}{D}\right)+13.889\cdot\left(\cfrac{d_i}{D}\right)^2$$
$C_4=-45+1.389\cdot\left(\cfrac{d_i}{D}\right)+13.889\cdot\left(\cfrac{d_i}{D}\right)^2$
Equations in LaTeX code
C_4=-45+1.389\cdot\left(\cfrac{d_i}{D}\right)+13.889\cdot\left(\cfrac{d_i}{D}\right)^2

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2+C_4\cdot\left(\cfrac{d}{D}\right)^3$$
$K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2+C_4\cdot\left(\cfrac{d}{D}\right)^3$
Equations in LaTeX code
K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2+C_4\cdot\left(\cfrac{d}{D}\right)^3

Maximum normal stress

$$σ_{max}=\cfrac{K_{tg}\cdot32\cdot M\cdot 10^3\cdot D}{π\cdot\left(D^4-d_i^4\right)}$$
$σ_{max}=\cfrac{K_{tg}\cdot32\cdot M\cdot 10^3\cdot D}{π\cdot\left(D^4-d_i^4\right)}$
Equations in LaTeX code
σ_{max}=\cfrac{K_{tg}\cdot32\cdot M\cdot 10^3\cdot D}{π\cdot\left(D^4-d_i^4\right)}
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